裂纹问题加权有限元法中的最优参数体

Q4 Chemical Engineering

Applied and Computational Mechanics Pub Date : 2021-09-15 DOI:10.22055/JACM.2021.38041.3142

S. Chamran, V. Rukavishnikov

{"title":"裂纹问题加权有限元法中的最优参数体","authors":"S. Chamran, V. Rukavishnikov","doi":"10.22055/JACM.2021.38041.3142","DOIUrl":null,"url":null,"abstract":"In this paper, a high-accuracy weighted finite element method is constructed and investigated for finding an approximate solution of the crack problem. We consider an approximation of the Lame system in the domain with the reentrant corner 2π at the boundary. A new concept of definition of the solution of the problem is introduced. It allows us to suppress the influence of the singularity on the accuracy of finding an approximate solution, in contrast to the classical approach. We have introduced a weight function into the basis of the finite element method. The accuracy of finding an approximate solution by the weighted finite element method depends on three input parameters. We created an algorithm and establish the body of optimal parameters in the weighted finite element method for the crack problem. The choice of parameters from this set allows us to accurately and stability find an approximate solution with the smallest deviation from the best error. This is required to generate industrial codes.","PeriodicalId":37801,"journal":{"name":"Applied and Computational Mechanics","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Body of Optimal Parameters in the Weighted Finite Element Method for the Crack Problem\",\"authors\":\"S. Chamran, V. Rukavishnikov\",\"doi\":\"10.22055/JACM.2021.38041.3142\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a high-accuracy weighted finite element method is constructed and investigated for finding an approximate solution of the crack problem. We consider an approximation of the Lame system in the domain with the reentrant corner 2π at the boundary. A new concept of definition of the solution of the problem is introduced. It allows us to suppress the influence of the singularity on the accuracy of finding an approximate solution, in contrast to the classical approach. We have introduced a weight function into the basis of the finite element method. The accuracy of finding an approximate solution by the weighted finite element method depends on three input parameters. We created an algorithm and establish the body of optimal parameters in the weighted finite element method for the crack problem. The choice of parameters from this set allows us to accurately and stability find an approximate solution with the smallest deviation from the best error. This is required to generate industrial codes.\",\"PeriodicalId\":37801,\"journal\":{\"name\":\"Applied and Computational Mechanics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied and Computational Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22055/JACM.2021.38041.3142\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Chemical Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied and Computational Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22055/JACM.2021.38041.3142","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Chemical Engineering","Score":null,"Total":0}

引用次数: 3

摘要

本文构造并研究了一种高精度的加权有限元方法，用于求解裂纹问题的近似解。我们考虑Lame系统在域中的一个近似，在边界处有凹角2π。引入了一个新的概念来定义问题的解决方案。与经典方法相比，它使我们能够抑制奇异性对寻找近似解精度的影响。我们在有限元法的基础上引入了一个权函数。加权有限元法求近似解的精度取决于三个输入参数。我们创建了一个算法，并在裂纹问题的加权有限元法中建立了最优参数体。从这个集合中选择参数使我们能够准确而稳定地找到与最佳误差偏差最小的近似解。这是生成工业代码所必需的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Body of Optimal Parameters in the Weighted Finite Element Method for the Crack Problem

In this paper, a high-accuracy weighted finite element method is constructed and investigated for finding an approximate solution of the crack problem. We consider an approximation of the Lame system in the domain with the reentrant corner 2π at the boundary. A new concept of definition of the solution of the problem is introduced. It allows us to suppress the influence of the singularity on the accuracy of finding an approximate solution, in contrast to the classical approach. We have introduced a weight function into the basis of the finite element method. The accuracy of finding an approximate solution by the weighted finite element method depends on three input parameters. We created an algorithm and establish the body of optimal parameters in the weighted finite element method for the crack problem. The choice of parameters from this set allows us to accurately and stability find an approximate solution with the smallest deviation from the best error. This is required to generate industrial codes.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applied and Computational Mechanics Engineering-Computational Mechanics

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

14 weeks

期刊介绍： The ACM journal covers a broad spectrum of topics in all fields of applied and computational mechanics with special emphasis on mathematical modelling and numerical simulations with experimental support, if relevant. Our audience is the international scientific community, academics as well as engineers interested in such disciplines. Original research papers falling into the following areas are considered for possible publication: solid mechanics, mechanics of materials, thermodynamics, biomechanics and mechanobiology, fluid-structure interaction, dynamics of multibody systems, mechatronics, vibrations and waves, reliability and durability of structures, structural damage and fracture mechanics, heterogenous media and multiscale problems, structural mechanics, experimental methods in mechanics. This list is neither exhaustive nor fixed.